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Quantized Control and Data Rate Constraints

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Encyclopedia of Systems and Control

Abstract

This article briefly describes the topic of quantized control with limited data rates. The focus is on the problem of stabilizing a linear time-invariant plant over a digital channel and the associated data rate theorems. It is shown that the deepest results in this area require a unified treatment of its communications and control aspects.

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Notes

  1. 1.

    Supported by Australian Research Council grant DP110102401

Bibliography

  • Baillieul J (1999) Feedback designs for controlling device arrays with communication channel bandwidth constraints. In: ARO workshop on smart structures, Pennsylvania State University

    Google Scholar 

  • Baillieul J (2002) Feedback designs in information-based control. In: Pasik-Duncan B (ed) Stochastic theory and control: proceedings of a workshop held in Lawrence, Kansas. Springer, pp 35–57

    Google Scholar 

  • Brockett RW, Liberzon D (2000) Quantized feedback stabilization of linear systems. IEEE Trans Autom Control 45(7):1279–1289

    Article  MathSciNet  Google Scholar 

  • Curry RE (1970) Estimation and control with quantized measurements. MIT, Cambridge

    Google Scholar 

  • Delchamps DF (1990) Stabilizing a linear system with quantized state feedback. IEEE Trans Autom Control 35:916–924

    Article  MathSciNet  Google Scholar 

  • Gersho A, Gray RM (1993) Vector quantization and signal compression. Kluwer, Boston

    Google Scholar 

  • Goodman DJ, Gersho A (1974) Theory of an adaptive quantizer. IEEE Trans Comms 22: 1037–1045

    Article  Google Scholar 

  • Hespanha J, Ortega A, Vasudevan L (2002) Towards the control of linear systems with minimum bit-rate. In: Proceedings of the 15th international symposium on the mathematical theory of networks and systems (MTNS), U. Notre Dame

    Google Scholar 

  • Liberzon D, Nesic D (2007) Input-to-state stabilization of linear systems with quantized state measurements. IEEE Trans Autom Control 52:767–781

    Article  MathSciNet  Google Scholar 

  • Matveev AS, Savkin AV (2007a) An analogue of Shannon information theory for detection and stabilization via noisy discrete communication channels. SIAM J Control Optim 46(4): 1323–1367

    Article  MathSciNet  Google Scholar 

  • Matveev AS, Savkin AV (2007b) Shannon zero error capacity in the problems of state estimation and stabilization via noisy communication channels. Int J Control 80:241–255

    Article  MathSciNet  Google Scholar 

  • Minero P, Coviello L, Franceschetti M (2013) Stabilization over Markov feedback channels: the general case. IEEE Trans Autom Control 58(2):349–362

    Article  MathSciNet  Google Scholar 

  • Nair GN (2012) A nonstochastic information theory for feedback. In: Proceedings of the IEEE conference decision and control, Maui, pp 1343–1348

    Google Scholar 

  • Nair GN (2013) A nonstochastic information theory for communication and state estimation. IEEE Trans Autom Control 58(6):1497–1510

    Article  Google Scholar 

  • Nair GN, Evans RJ (2000) Stabilization with data-rate-limited feedback: tightest attainable bounds. Syst Control Lett 41(1):49–56

    Article  MathSciNet  Google Scholar 

  • Nair GN, Evans RJ (2003) Exponential stabilisability of finite-dimensional linear systems with limited data rates. Automatica 39:585–593

    Article  MathSciNet  Google Scholar 

  • Nair GN, Evans RJ (2004) Stabilizability of stochastic linear systems with finite feedback data rates. SIAM J Control Optim 43(2):413–436

    Article  MathSciNet  Google Scholar 

  • Nair GN, Fagnani F, Zampieri S, Evans RJ (2007) Feedback control under data rate constraints: an overview. Proc IEEE 95(1):108–137. In special issue on Technology of Networked Control Systems

    Article  Google Scholar 

  • Sahai A, Mitter S (2006) The necessity and sufficiency of anytime capacity for stabilization of a linear system over a noisy communication link part 1: scalar systems. IEEE Trans Inf Theory 52(8): 3369–3395

    Article  MathSciNet  Google Scholar 

  • Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423, 623–656. Reprinted in ‘Claude Elwood Shannon Collected Papers’, IEEE Press, 1993

    Google Scholar 

  • Shannon CE (1956) The zero-error capacity of a noisy channel. IRE Trans Inf Theory 2:8–19

    Article  MathSciNet  Google Scholar 

  • Tatikonda S, Mitter S (2004) Control under communication constraints. IEEE Trans Autom Control 49(7):1056–1068

    Article  MathSciNet  Google Scholar 

  • Wong WS, Brockett RW (1999) Systems with finite communication bandwidth constraints II: stabilization with limited information feedback. IEEE Trans Autom Control 44:1049–1053

    Article  MathSciNet  Google Scholar 

  • You K, Xie L (2011) Minimum data rate for mean square stabilizability of linear systems with Markovian packet losses. IEEE Trans Autom Contr 56(4): 772–785

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical & Electronic Engineering, University of Melbourne, Melbourne, VIC, Australia

    Girish N. Nair

Authors
  1. Girish N. Nair
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Editor information

Editors and Affiliations

  1. Mechanical Engineering, Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Honeywell Automation and Control Solutions, Golden Valley, MN, USA

    Tariq Samad

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© 2015 Springer-Verlag London

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Nair, G.N. (2015). Quantized Control and Data Rate Constraints. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_149

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